Tri-pyramid Robot: Stiffness modeling of a 3-DOF translational parallel manipulator

This paper presents a 3-DOF (degree of freedom) translational parallel manipulator named the Tri-pyramid Robot. Compared to the developed 3-DOF translational parallel manipulators, the Tri-pyramid Robot is designed based on conical displacement subset to exhibit better kinematic characteristic. The inverse position solution is obtained through closed-loop constraint analysis and used to formulate the overall Jacobian matrix of constraints and actuations based on the theory of reciprocal screws. Furthermore, by considering the stiffness of all links, joints, actuators, fixed, and moving platforms, the output stiffness matrix of the Tri-pyramid Robot is derived by the transformations of loads and deformations in the closed-loop form. The relations between the virtual input-output displacements are analyzed by the overall Jacobian matrix and used to build the manipulator's stiffness model. Stiffness performance is evaluated by the extreme eigenvalues of the output stiffness matrix in the reachable workspace. By considering the variations of the structural parameters and the distribution of the output stiffness, the maximal stiffness workspace is obtained through numerical optimization, providing, thereby, basic constraints for the parametric design of the Tri-pyramid Robot.